Spread or concentrate? An Evidence Press briefing. Imagine adding up several random waiting times, such as the time until each of several machines next fails, each multiplied by a weight. Fix how variable the total is allowed to be. How small, and how large, can its higher averages, its moments, become? There is a tug of war. Putting all the weight on one waiting time keeps the average total small, but keeps that variable's long tail. Spreading the weight thins the tail, but raises the average. The answer for the smallest moment is a staircase. For exponential waiting times, one variable is best up to a moment order of about five point three two. Then two equal weights are best, then three, then four, one more at each step, growing in the long run like four tenths of the order. Brazitikos and Pandis conjectured this rule. It was already known for whole-number orders, for orders up to four by Brazitikos, Tang and Tkocz, and up to five in an AI-generated dossier. This paper proves it for every order, and for gamma waiting times of any shape. It also finds the largest moment. Equal weights on everything win up to a switch point. Beyond it, the best choice has one larger weight and the rest equal. With two variables the change is gradual; with three or more the best weights jump. Just above the switch, the equal-weight choice passes every local test for a maximum, yet is not the maximum. The results also cover sums of squared Gaussian variables, which appear in statistics and signal processing. The proofs are written out in full and backed by more than twenty-six thousand computer checks, openly archived with the paper. This is an anonymous, AI-assisted candidate. It has not been peer reviewed, independently reproduced or formally verified. Published on the third of November twenty twenty-six, its paper and evidence are linked from the Evidence Press release page. This briefing uses an AI-generated voice and is not additional scientific evidence.